Sample size requirement in analytical studies for similarity assessment

ABSTRACT

For the assessment of biosimilar products, the FDA recommends a stepwise approach for obtaining the totality-of-the-evidence for assessing biosimilarity between a proposed biosimilar product and its corresponding innovative biologic product. The stepwise approach starts with analytical studies for assessing similarity in critical quality attributes (CQAs), which are relevant to clinical outcomes at various stages of the manufacturing process. For CQAs that are the most relevant to clinical outcomes, the FDA requires an equivalence test be performed for similarity assessment based on an equivalence acceptance criterion (EAC) that is obtained using a single test value of some selected reference lots. In practice, we often have extremely imbalanced numbers of reference and test lots available for the establishment of EAC. In this case, to assist the sponsors, the FDA proposed an idea for determining the number of reference lots and the number of test lots required in order not to have imbalanced sample sizes when establishing EAC for the equivalence test based on extensive simulation studies. Along this line, this article not only provides statistical justification of Dong, Tsong, and Weng’s proposal, but also proposes an alternative method for sample size requirement for the Tier 1 equivalence test.     

Probability of passing dissolution acceptance criteria for an immediate release tablet

During development of solid dosage products, a pharmaceutical manufacturer is typically required to propose dissolution acceptance criteria unless the product falls into Biopharmaceutics Classification System (BCS) class I, in which case a disintegration test may be used. At the time of filing the new drug application (NDA) or common technical document (CTD), the manufacturer has already met with regulatory agencies to discuss and refine dissolution strategy. The dissolution acceptance criteria are based on stability and batch history data and are often arrived at by considering the percentage of batches that pass United States Pharmacopeia (USP) criteria at Stage 1 (S(1)), when in fact, the product is deemed unacceptable only when a batch fails USP criteria at Stage 3 (S(3)) [H. Saranadasa, Disso. Technol. 7 (2000) 6-7, 18 [1]]. Calculating the probability of passing (or failing) dissolution criteria at S(1), S(2), or S(3) can assist a manufacturer in determining appropriate acceptance criteria. This article discusses a general statistical method that was developed to assess the probability of passing the multistage USP test for dissolution and how it was applied to an immediate release tablet formulation. In this case, acceptance criteria were set and the analysis was conducted to assess the probabilities of passing or failing based on this acceptance criterion. Whether the acceptance criteria were relevant to the product was also considered. This mathematical approach uses a Monte Carlo simulation and considers a range of values for standard deviation and mean of historical data.     

Statistical evaluation of stability data: criteria for change-over-time and data variability

In a recently issued ICH Q1E guidance on evaluation of stability data of drug substances and products, the need to perform a statistical extrapolation of a shelf-life of a drug product or a retest period for a drug substance is based heavily on whether data exhibit a change-over-time and/or variability. However, this document suggests neither measures nor acceptance criteria of these two parameters. This paper demonstrates a useful application of simple statistical parameters for determining whether sets of stability data from either accelerated or long-term storage programs exhibit a change-over-time and/or variability. These parameters are all derived from a simple linear regression analysis first performed on the stability data. The p-value of the slope of the regression line is taken as a measure for change-over-time, and a value of 0.25 is suggested as a limit to insignificant change of the quantitative stability attributes monitored. The minimal process capability index, Cpk, calculated from the standard deviation of the regression line, is suggested as a measure for variability with a value of 2.5 as a limit for an insignificant variability. The usefulness of the above two parameters, p-value and Cpk, was demonstrated on stability data of a refrigerated drug product and on pooled data of three batches of a drug substance. In both cases, the determined parameters allowed characterization of the data in terms of change-over-time and variability. Consequently, complete evaluation of the stability data could be pursued according to the ICH guidance. It is believed that the application of the above two parameters with their acceptance criteria will allow a more unified evaluation of stability data.     

General Framework for Equivalence Testing over a Range of Linear Outcomes with CMC Applications

ABSTRACT

As per regulatory guidance, it is mandatory to demonstrate comparability before and after a change is made to an analytical method for commercial lot release or manufacturing process in the area of Chemistry, Manufacturing, and Controls. The change may include transfer assay or manufacturing process to a different location. Use of statistical methods to assess comparability before and after the change across the range of interest is a regulatory requirement. Regardless of the types of the changes, comparability is often demonstrated using analytical data collected pre- and post-change. For instance, assay transfer requires the demonstration of comparable assay performance over a range of expected responses. Although there are various methods used in practice or proposed in the published literature, there is no consensus on the best practice. For measurements that exhibit linearity in the outcome variable, a general statistical framework of equivalence testing is proposed. The equivalence test can be carried out either through Bayesian or frequentist analyses. The method is illustrated via several real-world examples.     

Application of the Modified Chi-Square Ratio Statistic in a Stepwise Procedure for Cascade Impactor Equivalence Testing

Equivalence testing of aerodynamic particle size distribution (APSD) through multi-stage cascade impactors (CIs) is important for establishing bioequivalence of orally inhaled drug products. Recent work demonstrated that the median of the modified chi-square ratio statistic (MmCSRS) is a promising metric for APSD equivalence testing of test (T) and reference (R) products as it can be applied to a reduced number of CI sites that are more relevant for lung deposition. This metric is also less sensitive to the increased variability often observed for low-deposition sites. A method to establish critical values for the MmCSRS is described here. This method considers the variability of the R product by employing a reference variance scaling approach that allows definition of critical values as a function of the observed variability of the R product. A stepwise CI equivalence test is proposed that integrates the MmCSRS as a method for comparing the relative shapes of CI profiles and incorporates statistical tests for assessing equivalence of single actuation content and impactor sized mass. This stepwise CI equivalence test was applied to 55 published CI profile scenarios, which were classified as equivalent or inequivalent by members of the Product Quality Research Institute working group (PQRI WG). The results of the stepwise CI equivalence test using a 25% difference in MmCSRS as an acceptance criterion provided the best matching with those of the PQRI WG as decisions of both methods agreed in 75% of the 55 CI profile scenarios.

Electronic supplementary material

The online version of this article (doi:10.1208/s12248-014-9698-0) contains supplementary material, which is available to authorized users.KEY Words: aerodynamic particle size distribution, bioequivalence, cascade impactor, chi-square ratio statistic, orally inhaled drug products     

Scientific Considerations for Generic Synthetic Salmon Calcitonin Nasal Spray Products

Under the Abbreviated New Drug Application pathway, a proposed generic salmon calcitonin nasal spray is required to demonstrate pharmaceutical equivalence and bioequivalence to the brand-name counterpart or the reference listed drug. This review discusses two important aspects of pharmaceutical equivalence for this synthetic peptide nasal spray product. The first aspect is drug substance sameness, in which a proposed generic salmon calcitonin product is required to demonstrate that it contains the same active ingredient as that in the brand-name counterpart. The second aspect is comparability in product- and process-related factors that may influence immunogenicity (i.e., peptide-related impurities, aggregates, formulation, and leachates from the container/closure system). The comparability of these factors helps to ensure the product safety, particularly with respect to immunogenicity. This review also highlights the key features of in vitro and/or in vivo studies for establishing bioequivalence for a solution nasal spray containing a systemically acting salmon calcitonin.     

A Risk-Based Approach to Setting Acceptance Criteria for Pharmaceutical Process Comparability

Purpose

Throughout the life cycle of a biotechnological drug product, changes and improvements of manufacturing processes are common. It is required by the regulatory bodies that manufacturers establish adequate and appropriate comparability between pre-change and post-change products. The goals of comparability assessments are to demonstrate the comparability and consistency of product quality before and after change and to demonstrate that the changes do not have an adverse effect on safety and efficacy of the drug products.

Methods

A well-planned and detailed comparability protocol may facilitate the approval of process changes and expedite the production and distribution of lifesaving drug products to patients. Analytical comparability is the foundation of all comparability exercise. Therefore, a sound comparability protocol should carefully select relevant critical quality attributes, prepare a flexible testing plan, and predefine appropriate acceptance criteria. Selection of analytical methods and acceptance criteria for determining comparability may be the most challenging step in the comparability study.

Results

In this article, a risk-based approach is proposed to setting the acceptance criteria for analytical comparability during the pharmaceutical process change. The proposed method is applied to a late-phase process comparability study, illustrating the value of using prior information and historical data.

Conclusion

The Bayesian methodology allows the manufacturer to utilize accumulated scientific knowledge and manufacture experience during the life cycle of pharmaceutical development and the risk assessment enables control of the probability of out-of-specification, thus protecting the patients’ risks.

     

Statistical Considerations in Setting Product Specifications

According to ICH Q6A (1999), a specification is defined as a list of tests, references to analytical procedures, and appropriate acceptance criteria, which are numerical limits, ranges, or other criteria for the tests described. For drug products, specifications usually consist of test methods and acceptance criteria for assay, impurities, pH, dissolution, moisture, and microbial limits, depending on the dosage forms. They are usually proposed by the manufacturers and subject to the regulatory approval for use. When the acceptance criteria in product specifications cannot be pre-defined based on prior knowledge, the conventional approach is to use data from a limited number of clinical batches during the clinical development phases. Often in time, such acceptance criterion is set as an interval bounded by the sample mean plus and minus two to four standard deviations. This interval may be revised with the accumulated data collected from released batches after drug approval. In this article, we describe and discuss the statistical issues of commonly used approaches in setting or revising specifications (usually tighten the limits), including reference interval, (Min, Max) method, tolerance interval, and confidence limit of percentiles. We also compare their performance in terms of the interval width and the intended coverage. Based on our study results and review experiences, we make some recommendations on how to select the appropriate statistical methods in setting product specifications to better ensure the product quality.     

Bioequivalence Assessment of Generic Products: An Innovative South African Approach

Concurrent with the implementation of new legislation mandating Generic Substitution in South Africa, a new set of guidelines for bioavailability and bioequivalence have been published. Since one of the main objectives of the new legislation in South Africa relating to Generic Substitution is to ensure that medicines of high quality, safety, and efficacy are made more accessible and more affordable to the wider public, the need to speed up approval of such multi-source products has become a regulatory priority. In order to facilitate this process, various bioequivalence issues have been addressed including important issues such as the acceptance criteria and associated bioequivalence intervals, use of a foreign reference product and the issue of assessing highly variable drugs (HVDs). In addition, dispensations have been made with respect to food effect assessment and variability relating to genetic polymorphism in drug metabolism (genotyping/phenotyping). Furthermore, the use of “old” biostudies submitted in support of an application is subject to expiry date. Acceptance of appropriate data requires that specific criteria such as C_max and AUC, in addition to the usual considerations, also meet the limits specified by the particular registration authority of the country where such products are intended to be marketed. Generally, these limits require that the 90% confidence interval (CI) for AUC and C_max test/reference ratios lies within the acceptance interval of 0.80–1.25 calculated using log-transformed data. While such acceptance criteria are, in general, ubiquitous, some differences in acceptance criteria do exist between various countries. The new guidelines for bioavailability/bioequivalence studies developed by the South African regulatory authority, the Medicines Control Council (MCC), makes provision for highly variable drugs and the use of a non-South African reference product. The MCC requires that the acceptance criterion for C_max ratios be set at 0.75–1.33 while maintaining AUC ratios at 0.80–1.25 using a 90% CI. Furthermore, provision is made to apply scaling based on average bioequivalence assessment and, as an interim measure, consideration has also been given to the use of a foreign reference product provided that equivalence between that product and the innovator product currently available on the South African market can be shown using in vitro testing.     

Formulation of a stable parenteral product; Clonidine Hydrochloride Injection

Clonidine Hydrochloride Injection (Duraclon) is a clear, colorless, preservative-free, pyrogen free, aqueous solution of clonidine hydrochloride. The indication for this product is for use as an adjunct in pain management, administered epidurally, when opiates are insufficient. The drug formulation was evaluated under both normal and stress conditions in the preformulation/formulation studies. The list of studies conducted includes a light sensitivity study, an oxygen sensitivity study, a pH/stability study, a stopper compatibility evaluation, a freeze-thaw study, and a stability study. Samples from the light, oxygen, pH/stability, and stability studies were evaluated for color, visual clarity, pH, potency, and chromatographic purity. Samples from the freeze-thaw study were evaluated for all of the above except chromatographic purity. The results for these studies demonstrate the stability of the product as formulated. The pH of this unbuffered product was consistently within the acceptance criteria. The product remained clear and colorless for the duration of each study. The values obtained for the potency and chromatographic purity assays showed no evidence of degradation. The reasons for the lack of degradation can be found in the molecular structure of the drug substance and the formulation of the drug product. Since the molecular structure is that of a Schiff base, it is theoretically possible, although difficult, to cleave the molecule. A catalyst would be required, and none of the possible catalysts are present in the formulation. The molecule could also be cleaved upon exposure to light, and the evidence indicates that the molecule does interact with light. This interaction is not to the degree, however, that product stability is affected. The formulation contains only the active drug substance and sodium chloride in water for injection with a pH of approximately 6. Although the product is unbuffered, the influence of the stoppers and glass vials upon the formulation pH was minimal. In addition, the stopper compatibility of the product is enhanced by the absence of chelating agents, preservatives, acids, and bases. Since the dilute concentrations of both the active and excipient are well below their solubility limits, no solubility related issues would be expected upon freezing and subsequent thawing. Clonidine Hydrochloride Injection, as formulated, does not require protection from light, oxygen, or freezing. The product shows acceptable stability within the pH range, and the rubber closure is compatible with the product. Real time stability data combined with statistical projections support a 36-month expiration date.     

A Review of: “Applied Survival Analysis: Regression Modeling of Time-to-Event Data, 2nd ed., by D. W. Hosmer,S. Lemeshow,and S. May”

For the statistical validation of surrogate endpoints, an alternative formulation is proposed for testing Prentice’s fourth criterion, under a bivariate normal model. In such a setup, the criterion involves inference concerning an appropriate regression parameter, and the criterion holds if the regression parameter is zero. Testing such a null hypothesis has been criticized in the literature since it can only be used to reject a poor surrogate, and not to validate a good surrogate. In order to circumvent this, an equivalence hypothesis is formulated for the regression parameter, namely the hypothesis that the parameter is equivalent to zero. Such an equivalence hypothesis is formulated as an alternative hypothesis, so that the surrogate endpoint is statistically validated when the null hypothesis is rejected. Confidence intervals for the regression parameter and tests for the equivalence hypothesis are proposed using bootstrap methods and small sample asymptotics, and their performances are numerically evaluated and recommendations are made. The choice of the equivalence margin is a regulatory issue that needs to be addressed. The proposed equivalence testing formulation is also adopted for other parameters that have been proposed in the literature on surrogate endpoint validation, namely, the relative effect and proportion explained.     

Prediction of the Long-Term Dissolution Performance of an Immediate-Release Tablet Using Accelerated Stability Studies

A slowdown in dissolution performance has been observed for an immediate release tablet formulation during long-term stability testing. The slowdown was successfully predicted using an accelerated stability study in which the dissolution was tested over a range of temperatures, humidity conditions and storage times. The slowdown was quantified using a calculated parameter referred to as the “acceleration factor” (AF); this is the degree by which the timescale (x-axis) of a dissolution profile needs to be scaled to overlay it on to the dissolution profile obtained at the initial timepoint. The “AF” approach was applicable because it was observed that the shape of the dissolution profile remains consistent even though different dissolution rates were obtained. Under the accelerated stability conditions, the AF is observed to follow an “exponential decay” curve. A predictive model for the long-term stability dissolution was obtained by modeling both the plateau level and the rate constant for the exponential decay curve as functions of temperature and humidity. The long-term stability of product A in packaging was successfully predicted using this model in combination with simulations of the changing relative humidity conditions inside the packaging.     

Clinical and statistical issues in therapeutic equivalence trials

Summary Absolute proof of efficacy can only be given by placebo controlled trials. It is, however, important to classify a drug within the spectrum of existing therapeutic alternatives and, where effective treatment is available, it may be imperative due to ethical considerations to demonstrate that one drug is as effective as another.The issue of therapeutic equivalence trials is discussed along the lines of the important items which should be defined in the protocol: a) the target parameter, which is the primary endpoint of the trial, b) the reference drug, which should be selected with respect to efficacy (superior to others), and safety (largest amount of data), c) the acceptance range, which depends on the primary endpoint, and its implication for the clinical endpoints of morbidity and mortality (the conventional acceptance range for bioequivalence trials does not apply), and d) the statistical procedures, which must take into consideration the unsuitability of the conventional power approach for confirming equivalence.In an equivalence trial, compared to those that are placebo-controlled, the proof that one drug is as effective as another relies much more upon the quality of conduct of the study according to Good Clinical Practice.     

Assessment of equivalence using a concordance correlation coefficient in a repeated measurements design

Some assay validation studies are conducted to assess agreement between repeated, paired continuous data measured on the same subject with different measurement systems. The goal of these studies is to show that there is an acceptable level of agreement between the measurement systems. Equivalence testing is a reasonable approach in assay validation. In this article, we use an equivalence-testing criterion based on a decomposition of a concordance correlation coefficient proposed by Lin (1989, 1992). Using a variance components approach, we develop bounds for conducting statistical tests using the proposed equivalence criterion. We conduct a simulation study to assess the performance of the bounds. The criteria are the ability to maintain the stated test size and the simulated power of the tests using these bounds. Bounds that perform well for small sample size are preferred. We present a computational example to demonstrate the methods described in the article.     

Performance Properties of the Population Bioequivalence Approach for In Vitro Delivered Dose for Orally Inhaled Respiratory Products

Regulatory agencies, industry, and academia have acknowledged that in vitro assessments serve a role in establishing bioequivalence for second-entry drug product approvals as well as innovator post-approval drug product changes. For orally inhaled respiratory products (OIPs), the issues of correctly analyzing in vitro data and interpreting the results within the broader context of therapeutic equivalence have garnered significant attention. One of the recommended statistical tests for in vitro data is the population bioequivalence method (PBE). The current literature for assessing the PBE statistical approach for in vitro data assumes a log normal distribution. This paper focuses on an assessment of that assumption for in vitro delivered dose. Concepts in development of a statistical model are presented. The PBE criterion and hypotheses are written for the case when data follows a normal distribution, rather than log normal. Results of a simulation study are reported, characterizing the performance of the PBE approach when data are expected to be normally distributed, rather than log normal. In these cases, decisions using the PBE approach are not consistent for the same absolute mean difference that the test product is from the reference product. A conclusion of inequivalency will occur more often if the test product dose is lower than the reference product for the same deviation from target. These features suggest that more research is needed for statistical equivalency approaches for in vitro data.     

Statistical assessment of between batch stability equivalence

A statistical method for testing the equivalence between batches regarding their stability is proposed. This method is based on the statistical linear model making use of a set of dummy variables to code the different batches. The method gives us the point estimates of the slope and zero intercept of one batch, and the differences and the corresponding confidence intervals with the remaining batches. In a second step, zero intercepts and slopes are estimated for all the batches. Stability equivalence assessment is based on the comparison of the confidence intervals for the differences between batches with the maximum difference allowable. The main advantages of this method are the possibility to compare several batches, to disclose the equivalence stability criteria from the statistical hypothesis about the equality between slopes, and the joint estimated of the residual variance whatever the decision to pool or not the data from different batches. This method is illustrated with two data set; the first one, previously published by other authors, involved six batches; the second data set include two batches and arose in a stability study of a commercial human insulin conducted in our laboratory.     

Equivalence concepts in clinical trials.

According to the recent ICH E9 Guidance Statistical Principles for Clinical Trials, efficacy is most convincingly established by demonstrating superiority to placebo, by showing superiority to an active control treatment or by demonstrating a dose-response relationship (so-called 'superiority' trials). For serious illnesses, a placebo-controlled trial may be considered unethical if a therapeutic treatment exists which has proven efficacious in relevant superiority trial(s). In that case, the scientifically sound use of an active treatment as a control should be considered. Active control trials designed to show that the efficacy of an investigational product is not relevantly worse than that of the active comparator are called 'non-inferiority' trials (1). After having confirmed non-inferiority, superiority of the alternative test treatment over the reference treatment can additionally be tested without the need to adjust the significance level (2). In contrast to cross-over bioequivalence trials based on pharmacokinetic endpoints such as AUC and Cmax, therapeutic equivalence and non-inferiority trials are based on clinical end-points. Therefore, they are often conducted as parallel group comparisons. It is important to note that the conclusion of equivalence or non-inferiority is based on the inclusion of the appropriate confidence interval in the equivalence acceptance range, and that it cannot be derived from a non-significant test result of the inappropriate null hypothesis of no treatment difference.